What is expand (n^2(n+1)^2)/4 ?

The solution to expand (n^2(n+1)^2)/4 is (n^4)/4+(n^3)/2+(n^2)/4

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expand (n^2(n+1)^2)/4

expand

\frac{n ^{2} ( n + 1 ) ^{2}}{4}

\frac{n ^{4}}{4} + \frac{n ^{3}}{2} + \frac{n ^{2}}{4}

Solution steps

\frac{n ^{2} ( n + 1 ) ^{2}}{4}

(n + 1)^{2} = n^{2} + 2 n + 1

= \frac{n ^{2} ( n ^{2} + 2 n + 1 )}{4}

Expand

n^{2} (n^{2} + 2 n + 1) : n^{4} + 2 n^{3} + n^{2}

= \frac{n ^{4} + 2 n ^{3} + n ^{2}}{4}

Apply the fraction rule:

\frac{a \pm b}{c} = \frac{a}{c} \pm \frac{b}{c}

\frac{n ^{4} + 2 n ^{3} + n ^{2}}{4} = \frac{n ^{4}}{4} + \frac{2 n ^{3}}{4} + \frac{n ^{2}}{4}

= \frac{n ^{4}}{4} + \frac{2 n ^{3}}{4} + \frac{n ^{2}}{4}

Cancel

\frac{2 n ^{3}}{4} : \frac{n ^{3}}{2}

= \frac{n ^{4}}{4} + \frac{n ^{3}}{2} + \frac{n ^{2}}{4}

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(- 1 - x) (- \frac{3}{2} - x) (- \frac{1}{2} - x)

(\frac{x ^{2}}{2} + \frac{a}{x})^{6}

2 sin^{2} (2 t) + 2 (e^{t} - 2)^{2}

What is expand (n^2(n+1)^2)/4 ?
The solution to expand (n^2(n+1)^2)/4 is (n^4)/4+(n^3)/2+(n^2)/4